$\begin{array}{1 1} (A)\;(-6,\infty)\\(B)\;(-\infty,4]\\(C)\;(-4,\infty]\\(D)\; (-9,\infty)\end{array} $

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- Same Quantity can be added (a subtracted ) to (from ) both sides of the inequality with out changing the sign of the in equality.
- Same positive quantities can be multiplied or divided to both side of the in equality with out changing the sign of the inequality.
- If same negative quantity is multiplied or divided to both sides of the inequality is reversed i.e $ '>'$ sign changes to $'<' $ and $'<'$ changes $'>'$ .

Step 1:

The given inequality

$3(2-x) \geq 2(1-x)$

=> $ 6-3x \geq 2-2x$

adding $2x$ on both sides of inequality.

=> $ 6-3x +2x \geq 2-2x+2x$

=> $ 6-x \leq 2$

adding $-6$ on both sides of inequality

=> $6-x -6 \geq 2-6$

$-x \geq -4$

Multiplying by a negative number -1 on both sides

$x \leq 4$

Step 2:

All real number less than and equal to 4 satisfy the given inequality .

The solution set is $(-\infty, 4]$

Hence B is the correct answer.

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